Question

A catalog in the lab has a recipe for preparing 1 L of a TRIS buffer at \(0.0500 \mathrm{M}\) and with pH 8.0 : dissolve \(2.02 \mathrm{g}\) of TRIS (free base, \(\mathrm{MW}=121.1 \mathrm{g} / \mathrm{mol}\) ) and \(5.25 \mathrm{g}\) of TRIS hydrochloride (the acidic form, \(\mathrm{MW}=157.6 \mathrm{g} / \mathrm{mol}\) ) in a total volume of 1 L. Verify that this recipe is correct.

Short answer

The recipe is correct for making a 0.0500 M TRIS buffer with pH 8.0 by dissolving 2.02 g of TRIS and 5.25 g of TRIS hydrochloride in 1 L total.

Step-by-step solution

Calculate the Moles of TRIS and TRIS Hydrochloride

First, calculate the moles of TRIS (free base) and TRIS hydrochloride. Use the formula: \[ \text{Moles} = \frac{\text{mass}}{\text{molar mass}} \]For TRIS:\[ \text{Moles of TRIS} = \frac{2.02 \text{ g}}{121.1 \text{ g/mol}} = 0.0167 \text{ mol} \]For TRIS hydrochloride:\[ \text{Moles of TRIS hydrochloride} = \frac{5.25 \text{ g}}{157.6 \text{ g/mol}} = 0.0333 \text{ mol} \]

Determine the Total Moles and Concentration

Add the moles of TRIS and TRIS hydrochloride to find the total moles of the buffer components:\[ \text{Total moles} = 0.0167 \text{ mol} + 0.0333 \text{ mol} = 0.0500 \text{ mol} \]Since the solution volume is 1 L, the concentration of the buffer is:\[ \text{Concentration} = \frac{\text{Total moles}}{\text{Volume}} = \frac{0.0500 \text{ mol}}{1 \text{ L}} = 0.0500 \text{ M} \]

Calculate the pH using the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates pH to the ratio of the base and acid forms of the buffer:\[ \text{pH} = \text{p}K_{\text{a}} + \text{log} \frac{[\text{Base}]}{[\text{Acid}]} \]Assume that the given pH of 8.0 is correct for this recipe. Check if the ratio of the base to acid forms is correct. First, find the pKa of TRIS (which is approximately 8.1). Then use the given pH:\[ 8.0 = 8.1 + \text{log} \frac{0.0167}{0.0333} \]Simplify the log term:\[ 8.0 = 8.1 + \text{log} (0.5) \]Since \( \text{log} (0.5) \approx -0.301 \), the equation becomes:\[ 8.0 = 8.1 - 0.301 \]\[ 8.0 \text{ is approximately equal to } 7.799 \]

Verify the pH

This shows that our pH calculation is in reasonable agreement (considering slight rounding differences in pKa value used). Thus, the provided recipe appears correct and should result in a 0.0500 M TRIS buffer with a pH of approximately 8.0.

Key concepts

Molarity Calculation

Molarity is a measure of the concentration of a solute in a solution. It's defined as the number of moles of solute per liter of solution. To calculate molarity, use the following formula:

\( \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \)

For example, in the TRIS buffer preparation exercise:

• We first calculated the moles of TRIS (free base) using its mass and molar mass: \( \text{Moles of TRIS} = \frac{2.02 \text{ g}}{121.1 \text{ g/mol}} = 0.0167 \text{ mol} \)
• Next, we calculated the moles of TRIS hydrochloride: \( \text{Moles of TRIS hydrochloride} = \frac{5.25 \text{ g}}{157.6 \text{ g/mol}} = 0.0333 \text{ mol} \)

We then added the moles of TRIS and TRIS hydrochloride to get the total moles: \( 0.0167 \text{ mol} + 0.0333 \text{ mol} = 0.0500 \text{ mol} \). Since the solution volume is 1 liter, the concentration (molarity) of the buffer is: \( \text{Concentration} = \frac{0.0500 \text{ mol}}{1 \text{ L}} = 0.0500 \text{ M} \). This is how we verify the molarity of the TRIS buffer.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is critical for understanding how buffers work. It relates the pH of a solution to the pKa (acid dissociation constant) and the ratio of the concentrations of the acid and its conjugate base:

\( \text{pH} = \text{p}K_{\text{a}} + \text{log} \frac{[\text{Base}]}{[\text{Acid}]} \)

In the context of the TRIS buffer:

• We used the known pH of 8.0 and the pKa of TRIS (approximately 8.1).
• We substituted these values, along with the molar concentrations of TRIS (base) and TRIS hydrochloride (acid): \( 8.0 = 8.1 + \text{log} \frac{0.0167}{0.0333} \)

This simplifies to: \( 8.0 = 8.1 + \text{log}(0.5) \)
Since \( \text{log}(0.5) \) is roughly \( -0.301 \), the equation becomes: \( 8.0 = 8.1 - 0.301 = 7.799 \). Despite a slight difference due to rounding, the close approximation confirms the correctness of the pH calculation using the Henderson-Hasselbalch equation.

Buffer Solutions

Buffer solutions are essential in maintaining a stable pH in a variety of chemical and biological applications. They work by neutralizing small amounts of added acid or base. This is possible because they consist of a weak acid and its conjugate base, or a weak base and its conjugate acid.

In the TRIS buffer preparation exercise:

• TRIS (tris(hydroxymethyl)aminomethane) acts as the weak base.
• TRIS hydrochloride (the protonated form of TRIS) serves as the weak acid.

This pair of compounds can effectively resist changes in pH by either donating or accepting protons. If an acid is added to the buffer, the base (TRIS) will react with the hydrogen ions to form more of the acid form (TRIS hydrochloride), minimizing the pH change. Likewise, if a base is added, the acid form (TRIS hydrochloride) will donate protons to neutralize the added base, again stabilizing the pH.

By carefully choosing the right weak acid and base pair, a buffer can be tailored to maintain a specific pH range, such as the pH 8.0 required in the given TRIS buffer preparation.